It sounds like a great project, and pretty original too!
You will have to make sure the transmitting coil is an air coil with no magnetic material, so you won't get losses from the transmitting coil.
Then you drive the coil with a LM1875 or other high freq very low distortion amp chip. And since that amp chip is basically an op-amp with + and - inputs, you can make it closed loop.
So you have a fixed amplitude input sinewave, easy enough, into the amp chip + input, and a non-inductive current sense resistor in series with the transmitting coil (on the ground side).
Then the signal from the current sense resistor is fed back into the - input of the amp chip so it regulates instananeous coil current to match the incoming sine wave.
It should work very well, the result willl be a fixed sine current ay any frequency. All it needs really is a signal generator and amp chip and the coil (and a few discretes).
It's a cool project, if you wanted to start your own thread and document your build I will subscribe to it.